Instability of a gravity current within a soap film

Goldstein, Raymond E. and Huppert, Herbert E. and Moffatt, H. Keith and Pesci, Adriana I. (2014) Instability of a gravity current within a soap film. Journal of Fluid Mechanics, 753. ISSN 1469-7645 DOI 10.1017/jfm.2014.395

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Abstract

One of the simplest geometries in which to study fluid flow between two soap films connected by a Plateau border is provided by a catenoid with a secondary film at its narrowest point. Dynamic variations in the spacing between the two rings supporting the catenoid lead to fluid flow between the primary and secondary films. When the rings are moved apart, while keeping their spacing within the overall stability regime of the films, after a rapid thickening of the secondary film the excess fluid in it starts to drain into the sloped primary film through the Plateau border at which they meet. This influx of fluid is accommodated by a local thickening of the primary film. Experiments described here show that after this drainage begins the leading edge of the gravity current becomes linearly unstable to a finite-wavelength fingering instability. A theoretical model based on lubrication theory is used to explain the mechanism of this instability. The predicted characteristic wavelength of the instability is shown to be in good agreement with experimental results. Since the gravity current advances into a film of finite, albeit microscopic, thickness this situation is one in which the regularization often invoked to address singularities at the nose of a thin film is physically justified.

Item Type: Article
Uncontrolled Keywords: 2014AREP; IA68;
Subjects: 99 - Other
Divisions: 99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 753
Identification Number: 10.1017/jfm.2014.395
Depositing User: Sarah Humbert
Date Deposited: 17 Oct 2014 17:45
Last Modified: 02 Nov 2014 00:21
URI: http://eprints.esc.cam.ac.uk/id/eprint/3137

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